how many shuffles...???

[dandy_don]

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My home game buddies and i debate how many shuffles are adequate between hands...what do you guys have to say? And do you favor one style of shuffling to another?


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7 shuffles

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7 is the minimum.

[CrazyN8]

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7 shuffles

[/ QUOTE ]I'm really happy that people throw this answer around. I mean, it's a cool result of Persi Diaconis, but most people giving the answer don't know the question.

For instance, what does "shuffle" mean? I know it's "cut & riffle", but it certainly matters how much variance there is in your cut AND riffle. (An interesting side note is that if your shuffle has NO variance, i.e. a perfect shuffle, then 8 "shuffles" will return the deck to the original state. A perfect shuffle is cutting 26/26, and then riffling alternate L,R,L,R,... perfectly. This clearly isn't randomizing at all.)

In the Diaconis paper, I think they assume that you cut with the binomial distribution (so the chance of cutting X cards is the chance of getting X Heads in 52 coint flips) and that you riffle proportional to the numbers of cards in each side. For instance, if you have 30 in the left side and 22 in the other, a left card will fall with probability 30/52. Then you repeat. These are reasonable assumptions, but of course they aren't perfect.

A much more important question is "What does 'adequate' mean?" There's no way to get it perfectly random; there's no such thing. However, with every iteration, we get closer to random. You just have to define how close you want it to get.

The way probabilists define "distance from random" is the "total variation distance". Basicially, you look at the set of decks that have the most incorrect chance of coming-up. If there's some set of decks D with the probability of getting one of those = |D|/52!+X, and this set has the largest such "X", then we say the TotalVariation Distance is X. The Diaconis paper defined some minumum X, and found that 7 shuffles get the T.V. dist to within X. But their choice of X is pretty arbitrary. (I forget how they justified their specific choice.)

My point is, there are lots of arbitrary decisions that went into this "7" number. The assumption of shuffle mechanics, of cut mechanics, and of "adequate". It sure makes good press, though. [img]/images/graemlins/smile.gif[/img]
-Sam

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wow, my head hurts! [img]/images/graemlins/grin.gif[/img]


so was 7 the right answer? [img]/images/graemlins/grin.gif[/img]

[CrazyN8]

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We have 30-minute blind levels and people who bitch if they don't get to play enough hands. So I avoid the wash.

I riffle, riffle, riffle, box, riffle, riffle, cut and deal.

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same here...bitching and all.

[bdypdx]

Scramble (wash), riffle, riffle, box, riffle. Cut.

Should be adequate.

[Yawkey]

Use two decks!! Most of the time hands will last long enough to have the next deck shuffled sufficantly to start a new hand right away. If you're not comfortable with your shuffle by the end of the hand, at most give it two more riffles, get a cut then deal. Even if you don't hit the magic number 7, one can certainly argue that shuffling various amounts adds to the randomness factor.

[Lottery Larry]

At least 7 or 8, preferably mixing up the size of the stack in each hand.

Adding a box/strip in the middle of the riffles doesn't hurt, either.

And, as I always advocate here, having the dealer cut and restack using 3-4 piles helps even more, on several fronts

[Lottery Larry]

Well, aren't YOU special?

Should we be scared that you know all of this, or pissed off at your arrogance? :P

Definitely appreciate all the comments...it certainly seems to be a 'feel' thing...what is right for your game...and the challenge appears to be striking a balance between thoroughness and efficiency

[Lottery Larry]

Maybe this is the source
http://weblog.fortnow.com/2004/03/persi-diaconis.html

"And you always thought mathematicians were serious people. Especially those at Ivy League universities like Harvard and Columbia. Well ...

Dr. Persi Diaconis and Dr. Dave Bayer have just come out with a study that may give you pause. They have found, after no end of riffling and counting, that it takes exactly seven ordinary, careless shuffles to give a totally random mix to ... "

Here's the 25-page paper, I believe:
http://www-stat.stanford.edu/~cgates...ers/Riffle.pdf

To the other poster complaining about a headache, check out 2A Basic Shuffling... and that's just the start!

The chart on page 3 might back up my 7-8 shuffles claim

[Lottery Larry]

Mainly, you don't want to crimp the flow of your home game, but you do want to add some security. Two decks gives you more of an opportunity to do both

I only occasionally wash, and occasionally count down the deck, during a night. The shuffles/cutting is done pretty much every hand, when possible.